Good stuff OP, nice to see Bayesian getting more attention recently. However, after reading your blog post, I can't help get the feeling this is how a natural frequentist would approach the problem. This method is effectively relying on known, statistical record of past events to form the priors.

Often a more useful and appropriate construct in the Bayesian world, is the use of a belief network or Bayesian Network. This is a probabilistic directed acyclic graph (DAG) that encodes priors, often in the form of subjective beliefs (yes subjectivity can be useful), including specific domain knowledge.

Common example: Consider a naive Bayesian classifier (a specialized form of belief network) that identifies individual pieces of spam. Do we arrive at the spam score by entering the probability of past events into a simple model based of the Bayes theorem formula?

No, it's trained using the vast amount of domain knowledge and pattern recognition (through our experience and own estimation of what 'spam' is) encoded in our minds, that provide the priors. Thus, even though there is a large amount of subjectivity involved, the overall result can objectively be measured, within a given utility function. Incidentally, this is often what makes many hardcore empiricists 'nervous', and hence avoid belief networks altogether.

Coming back to the Falcon 9: A piece of prior information outside the scope of historic safety records, for example, one of the lead engineers having a nagging doubt about a particular technical risk based on some observed phenomenon, could have an impact on the real world probability of the next event being a failure. (Which is a pretty useful thing to know!)

In fact, this exact scenario happened in 2003 with the disastrous destruction of the Space Shuttle Columbia. [1] An engineer spotted something wrong on previous flights, but management failed to heed the warning[2]. This could quite possibly have been averted, if a risk mitigation model were in place to account for such evidence.

Looking forward, it's quite possible to imagine a future where this decision making has been outsourced to a sophisticated AI based off a Bayes net, with far more accurate real world modeling of risk and failure probabilities, outclassing the amount of evidence and a human or committee could possibly hope to compete with.

While I've nothing against frequentist approaches (albeit Bayesian naturally makes more intuitive sense to me), a minor drawback is the reliance on the past to predict the future. For example if you had safety records on 1 million previous flights, then one might be tempted to say, "well that's that then, we now know objectively the probability of failures in the future -- end of story". But, the 1 000 001 flight may have been designed to fly on a completely different type of technology, that will change significantly change the safety record of space flight going forward for the next "x" years. Thus using a Bayesian approach account for all relevant priors, it would in theory be possible to reflect a more accurate probability for the 1 000 001 flight, before it took place.

Lastly Bayes nets are not the best tool for every job, and do have drawbacks in certain situations. They are vulnerable to things like Bayesian poisoning or confirmation bias. A Bayesian approach is only as useful as the ongoing real world relevancy and accuracy of the priors. As the old adage goes, GIGO - garbage in, garbage out.

[1] http://en.wikipedia.org/wiki/Space_Shuttle_Columbia_disaster

[2] http://www.guardian.co.uk/science/2003/jun/22/spaceexplorati...